There are many uses to which the Equation of Time has been used.
ASTRONOMICAL
Since Ptolemy's Almagest, written around 150 CE, was published, astronomers have been tabulating and using the Equation of Time. 
From Left to Right : Click to Enlarge (i) The 1493 Alfonsine Tables. (ii) 1496 Almanach Perpetuum, Abraham Zacut (iii) 1542 The Alfonsine Tables from Tabulae resolutae de supputandis siderum motibus clarissimi mathematici by Ioannes Virdung (iv) 1496 -  Epytoma Almagestum Ptolomei by Ioannis de Monte Regio (Regimontanus) (v) 1627 The Rudolphine Tables by Joannes Kepler - The first to reflect Kepler's own Elliptical theories.
NAVIGATIONAL
With introduction of accurate clocks (e.g. those introduced by John Harrison in 1759) and the publication of accurate tables of the Equation of Time (e.g. those by Christian Huygens in 1673 -  see below  - and subsequently the Nautical Almanac 1767 ), longitude could at last be simply calculated with sufficient precision for navigators.
It may be proper first to premise, that for all Calculations are made according to apparent Time by the Meridian of the Royal Observatory at Greenwich.
What are shown concerning the Equation of Time chiefly respects the Astronomer, the Mariner having little to do with it in computing his Longitude fro the Moon's Distances rom the Sun and Stars with the Help of the Ephemeris, all the Calculations therefore being adapted to apparent Time, the same which he will obtain by the Altitudes of the Sun or Stars in the Manner hereafter prescribed,
But if the Watches made upon Mr John Harrison's or other equivalent Principled should be brought into Use at Sea, the apparent Time deduced from apparent Time from the Altitude of the Sun must be corrected by the Equation of Time, and the mean Time found compared with that shown by the Watch, the Difference will be the Longitude in Time from the Meridian by which the Watch was set; as near as the Going of the Watch* can be depended upon. (* Going of the Watch = Accuracy)
Preface to the Nautical Almanac & Ephemeris 1st Edition 1767 by Nevil Maskelyn, Astronomer Royal
At a port of known longitude and where astronomers could measure time from the stars, the mariner would observe the firing of the noon cannon or the falling of the noon ball. At this moment, the chronometer was set to local mean time at that location.  When at sea, the navigator would used his sextant to measure when the sun reached its zenith. This was 12:00 hrs Solar Noon. 12:00 + EoT was thus Local Mean Noon. The difference between Local Mean Noon at the ship and Local Mean Time at the port as shown on the chronometer was the longitudinal difference between the two places in hours. This was multiplied by 15 to give the longitudinal difference in degrees.
Left to Right : Click to Enlarge : (i) 1973 Huygens' Horologium Oscillatorium  [note that days in this table for the Julian Calendar, 11 days different from the present Gregorian Calendar], (ii) The Marine Sextant. This works by optically bringing an image of the down towards the horizon. The navigator tracks the sun until it 'bumps' the horizon - that is the moment of solar noon (iii) The Naval Chronometer (iv) 1767 Page from Nautical Almanac & Astronomical Ephemeris

SUN COMPASSES
In the Second World War, Sun Compasses were developed to replace magnetic compasses in iron structured tanks & jeeps. They were used in the desert or jungles where maps were of no use. These were, in effect, stereoscopic sundials working backwards. One needed to know the time from radio broadcasts, then one could deduce the direction of North, To use, one had to have some idea of ones latitude. Two of the Sun Compasses had the Equation of Time built into their design.
Left to Right L Click to enlarge (i) & (ii) : Abrams Compass, made in the US  (iii) & (iv) : Cole Compass, made in South Africa (v) to (vii) : Bagnold Compass, made in the UK, shown being used in training and its instructions with the Equation of Time. (viii) World War II - Long Range Desert Group - see the Sun Compass on dash-board of first vehicle
See ISBN 9783842337022 The Bagnold Sun-Compass: Long Range Desert Group by Kuno Gross - available on Amazon
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